Generalized Correlations for Computing dH and dS for a Real Gas | Additional Documents & Tests for Civil Engineering (CE) PDF Download

The approach based on the use of the compressibility factors can be applied to the present instance to evolve generalized correlations for computing enthalpy and entropy changes for gases. We start with the Pitzer-type expression for the compressibility factor: 

Z =Z⁰ +ω Z¹                      ..(2.25)

Differentiating with respect to the reduced temperature we get:

                      ..(5.55)

Thus using eqn. 5.54 we may recast eqns. 5.37 and 5.38 as follows: 

                   ..(5.56)

                   ..(5.57)

Both the above equations may be rewritten individually as follows: 

                   ..(5.58)

                   ..(5.59a) 

And 

                   ..(5.59b)
 

Similarly: 

                   ..(5.60)

                   ..(5.61a)

                   ..(5.61b)

The term   in eqn. 5.59a constitutes the first order enthalpy departure, and  (in eqn. 5.59b) the second order (with respect to simple fluids) enthalpy departure at specified T_r and P_r. The same is true for the corresponding entropic terms provided by eqns. 5.61a and 5.61b.

The evaluation of the integrals in eqns. 5.59 to 5.62 may be carried out assuming an EOS. The most widely used approach is that of Lee and Kesler who employed a modified form of the BWR EOS (eqn. 2.17) to extend their generalized correlation to residual property estimation. Figs. 5.1 and 5.2 respectively provide values of (H^R)⁰/RT_{C an} (H^R)¹/RT_C respectively. Similar plots for the entropy terms (S^R)⁰ / R, an ( S^R)¹ /R are also available; however, here the plot of the entire entropy term (− S^R) as function of T_r and P_r is shown in fig. 5.3. Table of values of all the above (eqns. 5.59 to 5.62) are also available as functions of T r and P r Fig. at discrete intervals 

Fig. 5.1 Correlation of   drawn from tables of Lee-Kesler (Source: AIChE  J., pp. 510-527, 1975)

Fig. 5.2 Correlation of  drawn from tables of Lee-Kesler (Source: AIChE  J., pp. 510-527, 1975)

Figure 5.3 Generalized entropy departure functions using corresponding states.